ISBN: 3-540-65975-7
TITLE: Differentiability of Six Operators on Nonsmooth Functions and p-Variation
AUTHOR: Dudley, Richard M.; Norvaisa, Rimas
TOC:

Preface v
Part I. A survey on differentiability of six operators in relation to probability and statistics
Contents of Part I 1
1. Introduction; kinds of differentiability 2
2. The two-function composition operator (F, G)->F o G 12
3. The quantile (inverse) operator 17
4. The integration operator and Young integrals 20
5. The product integral 27
6. Probability and p-vaxiation 30
7. General and C-differentiability 35
8. The chain rule and concluding remarks 37
Appendices 43
References 67
Part II. Product integrals, Young integrals and p-variation
Abstract 73
Contents of Part II 73
1. Introduction 75
2. p-variation 81
3. Stieltjes and Young integrals 98
4. Product integrals 139
5. Indefinite product integrals 170
6. The logarithm operator 198
7. References 205
Part III. Differentiability of the composition and inverse operators for regulated and a.e. continuous functions
Abstract 209
Contents of Part III 209
1. Introduction 210
2. Regulated functions 213
3. Almost everywhere continuous functions 220
4. The quantile operator 222
5. The composition operator for real-valued functions 228
6. The composition operator for Banach-valued functions 234
Appendix 236
References 237
Part IV. Bibliographies on p-variation and phi-variation
by R. M. Dudley, R. Norvaia and Jinghua Qian
Abstract 241
Contents of Part IV 241
Introduction 242
Bibliography on p-variation 243
Bibliography on phi-variation 262
Subject Index 273
Author Index 275
END
